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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
3. Tests for Parallelograms
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Exercise 47 Page 503

Write an equation using given information.

x=4

Practice makes perfect

Let's begin with recalling that in a parallelogram diagonals bisect each other. Therefore, the distance between the point of intersection and vertex D is also 3x.

From the picture we can see that BD=6x. Since we know that AC is 40 and BD=35AC, we can write an equation to solve for x.

BD=6x
Substitute

BD= 3/5AC

3/5AC=6x
Substitute

AC= 40

3/5( 40)=6x
â–¼
Solve for x
MoveRightFacToNum

a/c* b = a* b/c

120/5=6x
ReduceFrac

a/b=.a /5./.b /5.

24/1=6x
DivByOne

a/1=a

24=6x
DivEqn

.LHS /6.=.RHS /6.

24/6=x
CalcQuot

Calculate quotient

4=x
RearrangeEqn

Rearrange equation

x=4

The quadrilateral ABCD is a parallelogram when x=4.

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